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Simplifying (2x + 7)(2x + 6) = 156 Reorder the terms: (7 + 2x)(2x + 6) = 156 Reorder the terms: (7 + 2x)(6 + 2x) = 156 Multiply (7 + 2x) * (6 + 2x) (7(6 + 2x) + 2x * (6 + 2x)) = 156 ((6 * 7 + 2x * 7) + 2x * (6 + 2x)) = 156 ((42 + 14x) + 2x * (6 + 2x)) = 156 (42 + 14x + (6 * 2x + 2x * 2x)) = 156 (42 + 14x + (12x + 4x2)) = 156 Combine like terms: 14x + 12x = 26x (42 + 26x + 4x2) = 156 Solving 42 + 26x + 4x2 = 156 Solving for variable 'x'. Reorder the terms: 42 + -156 + 26x + 4x2 = 156 + -156 Combine like terms: 42 + -156 = -114 -114 + 26x + 4x2 = 156 + -156 Combine like terms: 156 + -156 = 0 -114 + 26x + 4x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-57 + 13x + 2x2) = 0 Factor a trinomial. 2((-19 + -2x)(3 + -1x)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-19 + -2x)' equal to zero and attempt to solve: Simplifying -19 + -2x = 0 Solving -19 + -2x = 0 Move all terms containing x to the left, all other terms to the right. Add '19' to each side of the equation. -19 + 19 + -2x = 0 + 19 Combine like terms: -19 + 19 = 0 0 + -2x = 0 + 19 -2x = 0 + 19 Combine like terms: 0 + 19 = 19 -2x = 19 Divide each side by '-2'. x = -9.5 Simplifying x = -9.5Subproblem 2
Set the factor '(3 + -1x)' equal to zero and attempt to solve: Simplifying 3 + -1x = 0 Solving 3 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + -1x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -1x = 0 + -3 -1x = 0 + -3 Combine like terms: 0 + -3 = -3 -1x = -3 Divide each side by '-1'. x = 3 Simplifying x = 3Solution
x = {-9.5, 3}
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